World silver medallist Ellen Gandy was a surprise casualty in the 200m butterfly heats, but British team-mate Jemma Lowe progressed.
Gandy was considered a serious medal contender but faded badly.
Lowe's time of two minutes 7.64 seconds was the third quickest in the heats and she will return for the semi-finals.
"You can't doubt Ellen's commitment as she went off very quick. She was one of our medal contenders, but has had a nightmare. That was a good swim from Jemma Lowe, though, and we have got one in there with a chance."
GB's Michael Jamieson and Andrew Willis also made it to the semis of the 200m breaststroke, while the men's 4x200m freestyle relay team progressed.
Gandy, 20, who trains in Australia, has struggled pacing her races in the past and would have won gold at last year's World Championships in Shanghai but for tiring heavily in the final few metres.
Lowe was pleased with her performance in what was her first swim of the Games after she failed to qualify for the 100m butterfly.
"That's the best morning swim I have ever done and I am so happy," she told BBC Sport.
"The crowd was amazing. It kept me going and thinking positive."
While Gandy's podium prospects evaporated, Jamieson (2:08.98) and Willis (2:09.33) raised hopes that they could be in the mix for medals with the second and third quickest times in the 200m breaststroke heats.
Jamieson breaks British 200m breaststroke record
"It's easy to swim when you have some confidence," said Jamieson after setting a new British record.
"I think I have another gear, so I am looking forward to the semi-finals."
Willis added: "The heats were very quick, so I had to do everything to make it.
"I just want to go out tonight, do my best and get into the final."
In the men's 100m freestyle heats, Great Britain's only entrant, Adam Brown, failed to reach the next phase of the competition.
The United States-based swimmer, who was surprisingly left out of the 4x100m freestyle relay, produced a sluggish 49.20, which put him four places outside of a semi-final place.
The morning's session concluded with the men's 4x200m freestyle relay. The British team of David Carry, Ross Davenport, Rob Bale and Robbie Renwick battled into the final with the fifth-quickest time of 7:10.70.